The present invention relates to a pair of absorbent pants or a pant diaper for one-time use, comprising a crotch portion, front and back portions adjacent thereto, which are joined to form a waist portion surrounding the waist of the user, said portion being circumferentially elastic, an absorbent body, which is held tightly against the body of the user by the elastic waist portion. Such an absorbent pant diaper is known by our own Swedish patent application 9200663-4, having around the waist elastically extensible elements, for example elastically extensible strings, strips, film, fibre fabric, laminates or the like, which are designed to hold the pant diaper in place on the user and prevent it from slipping down from its intended position of use. In order to prevent the elastic tension from being uncomfortable for the user, the known pant diaper is provided with a large number of elastic elements, which, by virtue of their number, on one hand exert a sufficient total tightening force around the waist of the user for the pant diaper to not slip down, and, on the other hand, each does not exert an excessive local pressure on the user. However, the use of a large number of elastic elements involves a relatively high material cost. It is therefore desirable to be able to reduce the need for elastic elements in the waist portion of the pant diaper without having to deviate from the requirement that the pant diaper should stay up comfortably on the user.